5. (20 pt) Response to Harmonic Excitation: The system in Problem 3 is subject to an excitation f (t),as shown in Figure 2. The harmonic excitation is f(t)=10 e^{\dot{i} \omega

t} (a) Formulate the equation for the response of the forced vibration, x(t), based on the frequency response method. (b) Plot the frequency response (both magnitude and angle) using MATLAB. (c) Plot the excitation and response as a function of time if the harmonic excitation is f(t) =10 cos (3 t) N, the real part of equation (3) with a frequency of w = 3rad/s. Use MATLAB for plotting. Explain why the response of the forced vibration, x(t), obtained via the frequency response solution, does not start at the initial condition (for example, x(0) = -0.05 rad)? Is the true response supposed to start at the prescribed initial conditions? What does this mean about the solution obtained by the frequency response method? (e) Repeat Part (5c) for w = 6 rad/s and w = 12rad/s. Compare the results.